remainder

The remainder is what is left over after dividing. A remainder of three, no remainder, divide with a remainder.

Seventeen divided by five is three remainder two, and that remainder is the whole of what modular arithmetic works with — clocks, cryptography and calendars all run on it. In ordinary use, the remainder means the rest of anything: the remainder of the day. A remainder is also an unsold book sold off cheaply, and to remainder a title is to do that. Note remaining, remains.